2.10: Proficiency Exam
Proficiency Exam
For the following problems, simplify each of the expressions.
\(8(6−3)−5\cdot4+3(8)(2)\div4\cdot3\)
- Answer
-
\(40\)
\(\{2(1+7)^2\}^0\)
- Answer
-
\(1\)
\(\dfrac{1^8 + 4^0 + 3^3(1 + 4)}{2^2(2 + 15)}\)
- Answer
-
\(\dfrac{137}{68}\)
\(\dfrac{2 \cdot 3^4 - 10^2}{4 - 3} + \dfrac{5(2^2 + 3^2)}{11 - 6}\)
- Answer
-
\(75\)
Write the appropriate relation symbol (>, <) in place of the *.
\(5(2+11)∗2(8−3)−2\)
- Answer
-
>
For the following problems, use algebraic notation.
\((x-1)\) times \((3x \text{plus} 2)\)
- Answer
-
\((x-1)(3x+2)\)
A number divided by twelve is less than or equal to the same number plus four.
- Answer
-
\(\dfrac{x}{12} \le (x+4)\)
Locate the approximate position of \(−1.6\) on the number line.
- Answer
-
Is \(0\) a positive number, a negative number, neither, or both?
- Answer
-
Zero is neither positive nor negative.
Draw a portion of the number line and place points at all even integers strictly between 14 and 20.
- Answer
-
Draw a portion of the number line and place points at all real numbers strictly greater than −1 but less than or equal to 4.
- Answer
-
What whole numbers can replace x so that the following statement is true? \(-4 \le x \le 5\).
- Answer
-
\(0,1,2,3,4,5\)
Is there a largest real number between and including 6 and 10? If so, what is it?
- Answer
-
Yes, 10.
Use the commutative property of multiplication to write \(m(a+3)\) in an equivalent form.
- Answer
-
\((a + 3)m\)
Use the commutative properties to simplify \(3a4b8cd\).
- Answer
-
\(96abcd\)
Use the commutative properties to simplify \(4(x−9)2y(x−9)3y\).
- Answer
-
\(24y^2(x-9)^2\)
Simplify \(4\) squared times \(x\) cubed times \(y\) to the fifth.
- Answer
-
\(16x^3y^5\)
Simplify \((3)(3)(3)aabbbbabba(3)a\).
- Answer
-
\(81a^5b^6\)
For the following problems, use the rules of exponents to simplify each of the expressions.
\((3ab^2)^2(2a^3)^3\)
- Answer
-
\(71a^{11}b^7\)
\(\dfrac{x^{10}y^{12}}{x^2y^5}\)
- Answer
-
\(x^8y^7\)
\(\dfrac{52x^7y^{10}(y-x^4)^{12}(y+x)^5}{4y^6(y-x^4)^{10}(y+x)}\)
- Answer
-
\(13x^7y^4(y-x^4)^2(y+x)^4\)
\((x^ny^{3m}z^{2p})^4\)
- Answer
-
\(x^{4bn}y^{12m}z^{8p}\)
\(\dfrac{(5x+4)^0}{(3x^2-1)^0}\)
- Answer
-
\(1\)
\(\dfrac{x^∇x^□y^Δ}{x^Δy^∇}\)
- Answer
-
\(x^{∇+□-Δ}y^{Δ-∇}\)
What word is used to describe the letter or symbol that represents an unspecified member of a particular collection of two or more numbers that are clearly defined?
- Answer
-
A variable